Saturday, February 18, 2012

I went back to Bowles and Gintis to compare their results to those of Greg Clark that I posted about recently. The largest correlation reported by Bowles and Gintis for intergenerational earnings is 0.65, obtained when fathers' and sons' earnings are averaged over multiyear periods, whereas Clark finds a (roughly) 0.7 -- 0.8 correlation between parental and children's social and economic status. Clark was studying the past 200 years, using rare surnames, whereas Bowles and Gintis concentrated on the modern era. Even the lower value of 0.42 (more typical of results cited by Bowles and Gintis) implies some persistent stratification, as shown in the figure below.

Bowles and Gintis: ... The relevant facts on which most researchers now agree include the following: brothers’ incomes are much more similar than those of randomly chosen males of the same race and similar age differences; the incomes of identical twins are much more similar than fraternal twins or non-twin brothers; the children of well-off parents obtain more and higher quality schooling; and wealth inheritance makes an important contribution to the wealth owned by the offspring of the very rich. On the basis of these and other empirical regularities, it seems safe to conclude that the intergenerational transmission of economic status is accounted for by a heterogeneous collection of mechanisms, including the genetic and cultural transmission of cognitive skills and non-cognitive personality traits in demand by employers, the inheritance of wealth and income enhancing group memberships such as race, and the superior education and health status enjoyed by the children of higher status families. ...

Here are Bowles and Gintis on IQ and earnings:

We have located 65 estimates of the normalized regression coefﬁcient of a test score in an earnings equation in 24 different studies of U.S. data over a period of three decades. Our meta-analysis of these studies is presented in Bowles, Gintis, and Osborne (2002a). The mean of these estimates is 0.15, indicating that a standard deviation change in the cognitive score, holding constant the remaining variables (including schooling), changes the natural logarithm of earnings by about one-seventh of a standard deviation. By contrast, the mean value of the normalized regression coefﬁcient of years of schooling in the same equation predicting the natural log of earnings in these studies is 0.22, suggesting a somewhat larger independent effect of schooling. We checked to see if these results were dependent on the weight of overrepresented authors, the type of cognitive test used, at what age the test was taken and other differences among the studies and found no signiﬁcant effects. An estimate of the causal impact of childhood IQ on years of schooling (also normalized) is 0.53 (Winship and Korenman 1999). A rough estimate of the direct and indirect effect of IQ on earnings, call it b, is then b = 0.15+(0.53)(0.22) = 0.266.

... Using the values estimated above, we see that the contribution of genetic inheritance of IQ to the intergenerational transmission of income is (h2 (1+m)/2)(0.266)^2 = .035(1 + m) h2. If the heritability [h2] of IQ were 0.5 and the degree of assortation, m, were 0.2 (both reasonable, if only ball park estimates) and the genetic inheritance of IQ were the only mechanism accounting for intergenerational income transmission,then the intergenerational correlation would be 0.01, or roughly two percent the observed intergenerational correlation. Note the conclusion that the contribution of genetic inheritance of IQ is negligible is not the result of any assumptions concerning assortative mating or the heritability of IQ: the IQ genotype of parents could be perfectly correlated and the heritability of IQ 100 per cent without appreciably changing the qualitative conclusions. The estimate results from the fact that IQ is just not an important enough determinant of economic success.

[THESE RESULTS ARE SURPRISING SMALL. I'D GUESS THAT AVG IQ VARIES FROM ABOUT -.5 to -.75 SD AT 10TH PERCENTILE INCOME TO +.5 to +.75 SD (COLLEGE GRADUATES) AT 90TH PERCENTILE INCOME, SO CORRELATION OF PERHAPS 0.3 -- 0.5. I GUESS THE LITERATURE SUPPORTS 0.3.

BUT NOTE THAT AVERAGING INCOMES OVER EXTENDED PERIODS (LIKE 10 YEARS) INCREASES THE INTERGENERATIONAL CORRELATION SIGNIFICANTLY (I.E., FROM 0.4 TO .65, PRESUMABLY BY ELIMINATING SOME OF THE NOISE IN THE INCOME MEASUREMENT), SO ONE MIGHT EXPECT THE SAME FOR THE IQ-INCOME CORRELATION. (THE INTERGENERATIONAL STUFF IS COMING FROM SOMEWHERE!) SINCE THE IQ-INCOME CORRELATION ENTERS SQUARED, INCREASING IT HAS A BIG EFFECT.

IF WE TAKE THE INCOME-IQ CORRELATION AS 0.5 AND h2 = 0.5, THE CONTRIBUTION TO INTERGENERATIONAL CORRELATION IS (1/2)^3 = 0.125 WHICH IS A FOURTH OR FIFTH OF THE TOTAL.]

In the Terman study of gifted individuals, additional IQ above 135 or so had a relatively small effect on lifetime earnings: an increase of 15-20% for an additional SD of IQ. In contrast, personality factors such as Conscientiousness and Extraversion were strongly correlated with increased earnings (see figures at link above): an increase of about 50% from 10th to 90th percentile was observed. Note that personality factors are heritable, with h2 roughly 0.5 or so. These findings, which come from a high IQ sample and are thus affected by restriction of range, are nevertheless suggestive of effect sizes in the overall population.

While it doesn't appear that IQ alone can account for most of intergenerational earnings transmission, a combination of IQ, Conscientiousness, Extraversion, ambition, and traits related to social intelligence (even, physical attractiveness) likely play an important and heritable role. (Note the strong similarity in earnings of identical twins.) Perhaps this "success bundle" of traits is what elite (Ivy) holistic admissions is searching for? :-)

For more discussion of Bowles and Gintis, see GNXP 2011 and GNXP 2008. A numerical error in B&G is noted, but it doesn't change the qualitative conclusions.

I went back to Bowles and Gintis to compare their results to those of Greg Clark that I posted about recently. The largest correlation reported by Bowles and Gintis for intergenerational earnings is 0.65, obtained when fathers' and sons' earnings are averaged over multiyear periods, whereas Clark finds a (roughly) 0.7 -- 0.8 correlation between parental and children's social and economic status. Clark was studying the past 200 years, using rare surnames, whereas Bowles and Gintis concentrated on the modern era. Even the lower value of 0.42 (more typical of results cited by Bowles and Gintis) implies some persistent stratification, as shown in the figure below.

Bowles and Gintis: ... The relevant facts on which most researchers now agree include the following: brothers’ incomes are much more similar than those of randomly chosen males of the same race and similar age differences; the incomes of identical twins are much more similar than fraternal twins or non-twin brothers; the children of well-off parents obtain more and higher quality schooling; and wealth inheritance makes an important contribution to the wealth owned by the offspring of the very rich. On the basis of these and other empirical regularities, it seems safe to conclude that the intergenerational transmission of economic status is accounted for by a heterogeneous collection of mechanisms, including the genetic and cultural transmission of cognitive skills and non-cognitive personality traits in demand by employers, the inheritance of wealth and income enhancing group memberships such as race, and the superior education and health status enjoyed by the children of higher status families. ...

Here are Bowles and Gintis on IQ and earnings:

We have located 65 estimates of the normalized regression coefﬁcient of a test score in an earnings equation in 24 different studies of U.S. data over a period of three decades. Our meta-analysis of these studies is presented in Bowles, Gintis, and Osborne (2002a). The mean of these estimates is 0.15, indicating that a standard deviation change in the cognitive score, holding constant the remaining variables (including schooling), changes the natural logarithm of earnings by about one-seventh of a standard deviation. By contrast, the mean value of the normalized regression coefﬁcient of years of schooling in the same equation predicting the natural log of earnings in these studies is 0.22, suggesting a somewhat larger independent effect of schooling. We checked to see if these results were dependent on the weight of overrepresented authors, the type of cognitive test used, at what age the test was taken and other differences among the studies and found no signiﬁcant effects. An estimate of the causal impact of childhood IQ on years of schooling (also normalized) is 0.53 (Winship and Korenman 1999). A rough estimate of the direct and indirect effect of IQ on earnings, call it b, is then b = 0.15+(0.53)(0.22) = 0.266.

... Using the values estimated above, we see that the contribution of genetic inheritance of IQ to the intergenerational transmission of income is (h2 (1+m)/2)(0.266)^2 = .035(1 + m) h2. If the heritability [h2] of IQ were 0.5 and the degree of assortation, m, were 0.2 (both reasonable, if only ball park estimates) and the genetic inheritance of IQ were the only mechanism accounting for intergenerational income transmission,then the intergenerational correlation would be 0.01, or roughly two percent the observed intergenerational correlation. Note the conclusion that the contribution of genetic inheritance of IQ is negligible is not the result of any assumptions concerning assortative mating or the heritability of IQ: the IQ genotype of parents could be perfectly correlated and the heritability of IQ 100 per cent without appreciably changing the qualitative conclusions. The estimate results from the fact that IQ is just not an important enough determinant of economic success.

[THESE RESULTS ARE SURPRISING SMALL. I'D GUESS THAT AVG IQ VARIES FROM ABOUT -.5 to -.75 SD AT 10TH PERCENTILE INCOME TO +.5 to +.75 SD (COLLEGE GRADUATES) AT 90TH PERCENTILE INCOME, SO CORRELATION OF PERHAPS 0.3 -- 0.5. I GUESS THE LITERATURE SUPPORTS 0.3.

BUT NOTE THAT AVERAGING INCOMES OVER EXTENDED PERIODS (LIKE 10 YEARS) INCREASES THE INTERGENERATIONAL CORRELATION SIGNIFICANTLY (I.E., FROM 0.4 TO .65, PRESUMABLY BY ELIMINATING SOME OF THE NOISE IN THE INCOME MEASUREMENT), SO ONE MIGHT EXPECT THE SAME FOR THE IQ-INCOME CORRELATION. (THE INTERGENERATIONAL STUFF IS COMING FROM SOMEWHERE!) SINCE THE IQ-INCOME CORRELATION ENTERS SQUARED, INCREASING IT HAS A BIG EFFECT.

IF WE TAKE THE INCOME-IQ CORRELATION AS 0.5 AND h2 = 0.5, THE CONTRIBUTION TO INTERGENERATIONAL CORRELATION IS (1/2)^3 = 0.125 WHICH IS A FOURTH OR FIFTH OF THE TOTAL.]

In the Terman study of gifted individuals, additional IQ above 135 or so had a relatively small effect on lifetime earnings: an increase of 15-20% for an additional SD of IQ. In contrast, personality factors such as Conscientiousness and Extraversion were strongly correlated with increased earnings (see figures at link above): an increase of about 50% from 10th to 90th percentile was observed. Note that personality factors are heritable, with h2 roughly 0.5 or so. These findings, which come from a high IQ sample and are thus affected by restriction of range, are nevertheless suggestive of effect sizes in the overall population.

While it doesn't appear that IQ alone can account for most of intergenerational earnings transmission, a combination of IQ, Conscientiousness, Extraversion, ambition, and traits related to social intelligence (even, physical attractiveness) likely play an important and heritable role. (Note the strong similarity in earnings of identical twins.) Perhaps this "success bundle" of traits is what elite (Ivy) holistic admissions is searching for? :-)

For more discussion of Bowles and Gintis, see GNXP 2011 and GNXP 2008. A numerical error in B&G is noted, but it doesn't change the qualitative conclusions.